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1. A fish floats in water with its eye at the centre of an opaque walled full tank of water of circular cross section. When the fish look upwards, it can see a fish-eye view of the surrounding scene i.e. it is able to view the hemisphere of the scene above the water surface, and centred at the top of the tank. The diameter of the tank is 30 cm, and the critical angle for water is 48 degrees. At what depth below the surface of the water, d, must the fish be floating?
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Here's the answer, which I dont completely get. 13.5cm.

'From the fishes eye to the rim of the tank makes an angle of 48degrees with the vertical. Theemerging ray is horizontal (which is the requirement to see the horizon). Hence thedepth of the fish is, d x tan 48o = 15.0, giving d.'

I understand everything bar the 15. Where is the fifteen from??
2. (Original post by ChronicBoredom)
A fish floats in water with its eye at the centre of an opaque walled full tank of water of circular cross section. When the fish look upwards, it can see a fish-eye view of the surrounding scene i.e. it is able to view the hemisphere of the scene above the water surface, and centred at the top of the tank. The diameter of the tank is 30 cm, and the critical angle for water is 48 degrees. At what depth below the surface of the water, d, must the fish be floating?
Spoiler:
Show
Here's the answer, which I dont completely get. 13.5cm.

'From the fishes eye to the rim of the tank makes an angle of 48degrees with the vertical. Theemerging ray is horizontal (which is the requirement to see the horizon). Hence thedepth of the fish is, d x tan 48o = 15.0, giving d.'

I understand everything bar the 15. Where is the fifteen from??
Sketch the situation and identify the right-angle triangle. tan 48 = opposite/adjacent where adjancent is d and opposite is the radius = diameter/2 = 30/2 = 15.
3. (Original post by Zacken)
Sketch the situation and identify the right-angle triangle. tan 48 = opposite/adjacent where adjancent is d and opposite is the radius = diameter/2 = 30/2 = 15.

I did sketch it... Why is the length of the cylinder divided by two equal to the radius of the circle. Aren't they independant things??
4. Oh wow, I didn't read the ques properly. The length of the tank is equal to the diameter of the circle (cross sectional area) of the tank I take it?
5. (Original post by ChronicBoredom)
I did sketch it... Why is the length of the cylinder divided by two equal to the radius of the circle. Aren't they independant things??
Diameter, not length.
6. (Original post by ChronicBoredom)
Oh wow, I didn't read the ques properly. The length of the tank is equal to the diameter of the circle (cross sectional area) of the tank I take it?
Exactement, although I would say more the diameter of the tank instead of the length.

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